"I am thankful for all those difficult people in my life, they have shown me exactly who I do not want to be." - Unknown
The label 'difficult person' has a lot of assumptions that aren't necessarily true. They may be seen as people who are out to get you, want to hurt you, are always difficult, etc. Some of these points may be true in certain cases, but common sense dictates that people care much more about themselves than to go out of their way to make you miserable. Oftentimes, some people tend to be more difficult than others, to generalize to a variety of situations, but that's not up to you to fix. Your goal is to deal with the situation and protect yourself from any potential toxic influence from this person.
1. You can't make a difficult person an easy person (even if you can diffuse the tension temporarily)
We can convince ourselves that if we just make them see your way then it'll all work out. Even if you believe you are the more reasonable one in this situation, that may not be true from their point of view — they may have a whole host of reasons why they are not agreeable at the moment, a lot of which they likely don't want to share. It's not up to you to change them. Some people simply don't work well together. For example, I once collaborated with an individual with a polar opposite personality — it's not that either of us were bad people, but rather we simply couldn't understand each other and it was hard to break assumptions we had about the other person.
2. Both of you play a role
Whether someone is 'at fault' for a difficult situation isn't going to make the situation better. People have a tendency to believe that they are in the right and that you are the one in the wrong, which ends up pushing the responsibility for the situation onto the other person. Both of you have to step up and take responsibility, but even if the other person doesn't, you need to step up and take that role. This means that you're willing to work with them and listen to their side of the story, even if it can be difficult to do so. Take responsibility for the part you've played, even if that means simply finding out what they think you should take responsibility for.
3. You're allowed to disengage with them if all else fails (especially if --or even if they're taking an emotional toll on you
Sometimes you can't get through to an individual. That doesn't mean you did anything wrong, but rather there's an issue that's beyond your control right now. We have a tendency to seek out these sort of advice articles because we want to find out how to control our situations, but sometimes there simply isn't an answer and you need to back away. Disengage. Refuse to take it. Your emotional health is one of your utmost priorities, and no one should compromise that.
4. Your logic isn't their logic
Everyone has a different set of knowledge and experiences which colors their logic. Someone could act in a manner completely nonsensical to you, but that may make complete sense from their point of view. You simply don't know. For example, an individual I collaborated with saw that my double-checking all of our work with them was a sign that I wasn't paying attention or wasn't taking as much responsibility on the project, whereas I saw it the complete opposite. I wanted to make sure we were both on the same page, but for whatever reason, that didn't come across to him.
5. Be frustrated, upset, or angry if that's how you feel (but there's a limit)
It's not necessary to pretend that you're 100% happy with an arrangement. You don't have to react to what someone says or does with a smile. That's not true to yourself, but also that gives the other person the wrong message: that what they're doing or saying is okay to you. You may think that you're hinting towards your discomfort, but it's hard to really know what other people think about a situation. Expressing a reasonable amount of emotion can help communication. For example, you could say: "I feel frustrated when ____ happens because I think ___." Make sure you don't frame it as criticism but focus more on "I" statements. However, it's definitely not okay to blow up at someone, save for extreme circumstances.
6. It's impossible to know their entire situation
People have issues in their lives that you don't know about. Period. Giving them the benefit of the doubt can also give you peace of mind. For example, there were definitely people in my life who were affected by my depression and weren't aware of it. At times, I've likely been less alert and less able to give 100% to a team effort, even if I wanted to do better — it may have come off like I didn't care or I was lazy, even if that wasn't true. I can transfer this situation to how I think about other people, and allow myself to have some compassion and understanding that may not necessarily have come through.
7. They likely think that YOU'RE the difficult person
This can be hard to hear. People think that they're right and you're wrong — it's harder to acknowledge that you could also be a difficult person to the difficult person in your life. The tension you feel between yourself and another person hardly is felt one way. They're likely in a similar position in which they're asking themselves: how do I deal with this difficult person? It sounds almost comical, but it's true.